Created By : Jatin Gogia
Reviewed By : Rajasekhar Valipishetty
Last Updated : Apr 06, 2023
Make use of GCF Calculator to quickly find the Greatest Common Factor of numbers 168, 174 i.e. 6 largest integer by which both the numbers can be divided.
Greatest common factor (GCF) of 168 and 174 is 6.
GCF(168,174) = 6
Greatest common factor or Greatest common divisor (GCD) can be calculated in following way;
Prime Factorization of 168
2 | 168 |
2 | 84 |
2 | 42 |
3 | 21 |
7 | 7 |
1 |
Prime factors of 168 are 2,3,7. Prime factorization of 168 in exponential form is:
168 = 23×31×71
Prime Factorization of 174
2 | 174 |
3 | 87 |
29 | 29 |
1 |
Prime factors of 174 are 2,3,29. Prime factorization of 174 in exponential form is:
174 = 21×31×291
∴ So by taking common prime factors GCF of 168 and 174 is 6
Factors of 168
List of positive integer factors of 168 that divides 168 without a remainder.
1,2,3,4,6,7,8,12,14,21,24,28,42,56,84,168
Factors of 174
List of positive integer factors of 174 that divides 174 without a remainder.
1,2,3,6,29,58,87,174
Greatest Common Factor
We found the factors and prime factorization of 168 and 174. The biggest common factor number is the GCF number.
So the greatest common factor 168 and 174 is 6.
Also check out the Least Common Multiple of 168 and 174
(i) The GCF of 168 and 174 is associative
GCF of 168 and 174 = GCF of 174 and 168
1. What is the GCF of 168 and 174?
Answer: GCF of 168 and 174 is 6.
2. What are the Factors of 168?
Answer: Factors of 168 are 1, 2, 3, 4, 6, 7, 8, 12, 14, 21, 24, 28, 42, 56, 84, 168. There are 16 integers that are factors of 168. The greatest factor of 168 is 168.
3. What are the Factors of 174?
Answer: Factors of 174 are 1, 2, 3, 6, 29, 58, 87, 174. There are 8 integers that are factors of 174. The greatest factor of 174 is 174.
4. How to Find the GCF of 168 and 174?
Answer:
Greatest Common Factor of 168 and 174 = 6
Step 1: Find the prime factorization of 168
168 = 2 x 2 x 2 x 3 x 7
Step 2: Find the prime factorization of 174
174 = 2 x 3 x 29
Step 3: Multiply those factors both numbers have in common in steps i) or ii) above to find the gcf:
GCF = 2 x 3 = 6
Step 4: Therefore, the greatest common factor of 168 and 174 is 6